Download or read book Weakly Nonlinear Systems written by Federico Beffa and published by Springer Nature. This book was released on 2023-10-26 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The open access book covers a large class of nonlinear systems with many practical engineering applications. The approach is based on the extension of linear systems theory using the Volterra series. In contrast to the few existing treatments, our approach highlights the algebraic structure underlying such systems and is based on Schwartz’s distributions (rather than functions). The use of distributions leads naturally to the convolution algebras of linear time-invariant systems and the ones suitable for weakly nonlinear systems emerge as simple extensions to higher order distributions, without having to resort to ad hoc operators. The result is a much-simplified notation, free of multiple integrals, a conceptual simplification, and the ability to solve the associated nonlinear differential equations in a purely algebraic way. The representation based on distributions not only becomes manifestly power series alike, but it includes power series as the description of the subclass of memory-less, time-invariant, weakly nonlinear systems. With this connection, many results from the theory of power series can be extended to the larger class of weakly nonlinear systems with memory. As a specific application, the theory is specialised to weakly nonlinear electric networks. The authors show how they can be described by a set of linear equivalent circuits which can be manipulated in the usual way. The authors include many real-world examples that occur in the design of RF and mmW analogue integrated circuits for telecommunications. The examples show how the theory can elucidate many nonlinear phenomena and suggest solutions that an approach entirely based on numerical simulations can hardly suggest. The theory is extended to weakly nonlinear time-varying systems, and the authors show examples of how time-varying electric networks allow implementing functions unfeasible with time-invariant ones. The book is primarily intended for engineering students in upper semesters and in particular for electrical engineers. Practising engineers wanting to deepen their understanding of nonlinear systems should also find it useful. The book also serves as an introduction to distributions for undergraduate students of mathematics.

Download or read book Weakly Connected Nonlinear Systems written by Anatoly Martynyuk and published by CRC Press. This book was released on 2012-11-20 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion provides a systematic study on the boundedness and stability of weakly connected nonlinear systems, covering theory and applications previously unavailable in book form. It contains many essential results needed for carrying out research on nonlinear systems of weakly connected equations. After supplying the necessary mathematical foundation, the book illustrates recent approaches to studying the boundedness of motion of weakly connected nonlinear systems. The authors consider conditions for asymptotic and uniform stability using the auxiliary vector Lyapunov functions and explore the polystability of the motion of a nonlinear system with a small parameter. Using the generalization of the direct Lyapunov method with the asymptotic method of nonlinear mechanics, they then study the stability of solutions for nonlinear systems with small perturbing forces. They also present fundamental results on the boundedness and stability of systems in Banach spaces with weakly connected subsystems through the generalization of the direct Lyapunov method, using both vector and matrix-valued auxiliary functions. Designed for researchers and graduate students working on systems with a small parameter, this book will help readers get up to date on the knowledge required to start research in this area.

Download or read book Weakly Connected Nonlinear Systems written by Anatoly Martynyuk and published by CRC Press. This book was released on 2016-04-19 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion provides a systematic study on the boundedness and stability of weakly connected nonlinear systems, covering theory and applications previously unavailable in book form. It contains many essential results needed for carrying out research on nonlinear systems of weakly connected

Download or read book Variational Principles in Classical Mechanics written by Douglas Cline and published by . This book was released on 2018-08 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th - 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering.This book introduces variational principles and their application to classical mechanics. The relative merits of the intuitive Newtonian vectorial formulation, and the more powerful variational formulations are compared. Applications to a wide variety of topics illustrate the intellectual beauty, remarkable power, and broad scope provided by use of variational principles in physics.The second edition adds discussion of the use of variational principles applied to the following topics:(1) Systems subject to initial boundary conditions(2) The hierarchy of related formulations based on action, Lagrangian, Hamiltonian, and equations of motion, to systems that involve symmetries.(3) Non-conservative systems.(4) Variable-mass systems.(5) The General Theory of Relativity.Douglas Cline is a Professor of Physics in the Department of Physics and Astronomy, University of Rochester, Rochester, New York.

Download or read book Nonlinear Systems Analysis written by M. Vidyasagar and published by SIAM. This book was released on 2002-01-01 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature. The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Audience: this text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers and practitioners working in areas such as robotics, spacecraft control, motor control, and power systems.

Download or read book Normal Modes and Localization in Nonlinear Systems written by Alexander F. Vakakis and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nonlinear normal modes of a parametrically excited cantilever beam are constructed by directly applying the method of multiple scales to the governing integral-partial differential equation and associated boundary conditions. The effect of the inertia and curvature nonlin earities and the parametric excitation on the spatial distribution of the deflection is examined. The results are compared with those obtained by using a single-mode discretization. In the absence of linear viscous and quadratic damping, it is shown that there are nonlinear normal modes, as defined by Rosenberg, even in the presence of a principal parametric excitation. Furthermore, the nonlinear mode shape obtained with the direct approach is compared with that obtained with the discretization approach for some values of the excitation frequency. In the single-mode discretization, the spatial distribution of the deflection is assumed a priori to be given by the linear mode shape ¢n, which is parametrically excited, as Equation (41). Thus, the mode shape is not influenced by the nonlinear curvature and nonlinear damping. On the other hand, in the direct approach, the mode shape is not assumed a priori; the nonlinear effects modify the linear mode shape ¢n. Therefore, in the case of large-amplitude oscillations, the single-mode discretization may yield inaccurate mode shapes. References 1. Vakakis, A. F., Manevitch, L. I., Mikhlin, Y. v., Pilipchuk, V. N., and Zevin A. A., Nonnal Modes and Localization in Nonlinear Systems, Wiley, New York, 1996.

Download or read book Mathematical Methods for Scientists and Engineers written by Peter B. Kahn and published by Courier Corporation. This book was released on 2004-01-01 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Appropriate for advanced undergraduate and graduate students in a variety of scientific and engineering fields, this text introduces linear and nonlinear problems and their associated models. The first part covers linear systems, emphasizing perturbation or approximation techniques and asymptotic methods. The second part comprises nonlinear problems, including weakly nonlinear oscillatory systems and nonlinear difference equations. The two parts, both of which include exercises, merge smoothly, and many of the nonlinear techniques arise from the study of the linear systems. 1990 edition. 70 figures. 4 tables. Appendix. Index.

Download or read book The Mechanics of Nonlinear Systems with Internal Resonances written by Arkadiy I. Manevich and published by World Scientific. This book was released on 2005 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most important features of nonlinear systems with several degrees of freedom is the presence of internal resonances at certain relations between natural frequencies of different modes. This monograph is the first book devoted predominantly to internal resonances in different mechanical systems including those of practical importance.The main purpose is to consider the internal resonances from the general point of view and to elucidate their role in applied nonlinear dynamics by using an efficient approach based on introducing the complex representation of equations of motion (together with the multiple scale method). Considered here are autonomous and nonautonomous discrete two-degree-of-freedom systems, infinite chains of particles, and continuous systems, including circular rings and cylindrical shells. Specific attention is paid to the case of one-to-one internal resonance in systems with cubic nonlinearities. Steady-state and nonstationary regimes of motion, interaction of the internal and external resonances at forced oscillations, and bifurcations of steady-state modes and their stability are systematically studied.

Download or read book Iterative Methods for Solving Nonlinear Equations and Systems written by Juan R. Torregrosa and published by MDPI. This book was released on 2019-12-06 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.

Download or read book Dynamics of Lattice Materials written by A. Srikantha Phani and published by John Wiley & Sons. This book was released on 2017-09-25 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a comprehensive introduction to the dynamic response of lattice materials, covering the fundamental theory and applications in engineering practice Offers comprehensive treatment of dynamics of lattice materials and periodic materials in general, including phononic crystals and elastic metamaterials Provides an in depth introduction to elastostatics and elastodynamics of lattice materials Covers advanced topics such as damping, nonlinearity, instability, impact and nanoscale systems Introduces contemporary concepts including pentamodes, local resonance and inertial amplification Includes chapters on fast computation and design optimization tools Topics are introduced using simple systems and generalized to more complex structures with a focus on dispersion characteristics

Download or read book Advances in Analog Circuits written by Esteban Tlelo-Cuautle and published by BoD – Books on Demand. This book was released on 2011-02-02 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights key design issues and challenges to guarantee the development of successful applications of analog circuits. Researchers around the world share acquired experience and insights to develop advances in analog circuit design, modeling and simulation. The key contributions of the sixteen chapters focus on recent advances in analog circuits to accomplish academic or industrial target specifications.

Download or read book On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation written by M. Escobedo and published by American Mathematical Soc.. This book was released on 2015-10-27 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.

Download or read book Nonlinear Waves in Integrable and Non integrable Systems written by Jianke Yang and published by SIAM. This book was released on 2010-12-02 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Waves in Integrable and Nonintegrable Systems presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind. This book is intended for researchers and graduate students working in applied mathematics and various physical subjects where nonlinear wave phenomena arise (such as nonlinear optics, Bose-Einstein condensates, and fluid dynamics).

Download or read book Localization Energy Transfer in Nonlinear Systems written by Robert Sinclair MacKay and published by World Scientific. This book was released on 2003 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference was the third meeting organized in the framework of the European LOCNET project. The main topics discussed by this international research collaboration were localization by nonlinearity and spatial discreteness, and energy transfer (in crystals, biomolecules and Josephson arrays).

Download or read book Wireless Receiver Architectures and Design written by Tony J. Rouphael and published by Academic Press. This book was released on 2014-06-17 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wireless Receiver Architectures and Design presents the various designs and architectures of wireless receivers in the context of modern multi-mode and multi-standard devices. This one-stop reference and guide to designing low-cost low-power multi-mode, multi-standard receivers treats analog and digital signal processing simultaneously, with equal detail given to the chosen architecture and modulating waveform. It provides a complete understanding of the receiver's analog front end and the digital backend, and how each affects the other. The book explains the design process in great detail, starting from an analysis of requirements to the choice of architecture and finally to the design and algorithm development. The advantages and disadvantages of each wireless architecture and the suitability to a standard are given, enabling a better choice of design methodology, receiver lineup, analog block, and digital algorithm for a particular architecture. Whether you are a communications engineer working in system architecture and waveform design, an RF engineer working on noise and linearity budget and line-up analysis, a DSP engineer working on algorithm development, or an analog or digital design engineer designing circuits for wireless transceivers, this book is your one-stop reference and guide to designing low-cost low-power multi-mode multi-standard receivers. The material in this book is organized and presented to lead you from applied theory to practical design with plenty of examples and case studies drawn from modern wireless standards. - Provides a complete description of receiver architectures together with their pros and cons, enabling a better choice of design methodology - Covers the design trade-offs and algorithms between the analog front end and the digital modem – enabling an end-to-end design approach - Addresses multi-mode multi-standard low-cost, low-power radio design – critical for producing the applications for Smart phones and portable internet devices

Download or read book Nonlinear System Identification written by Stephen A. Billings and published by John Wiley & Sons. This book was released on 2013-07-29 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice. Includes coverage of: The NARMAX (nonlinear autoregressive moving average with exogenous inputs) model The orthogonal least squares algorithm that allows models to be built term by term where the error reduction ratio reveals the percentage contribution of each model term Statistical and qualitative model validation methods that can be applied to any model class Generalised frequency response functions which provide significant insight into nonlinear behaviours A completely new class of filters that can move, split, spread, and focus energy The response spectrum map and the study of sub harmonic and severely nonlinear systems Algorithms that can track rapid time variation in both linear and nonlinear systems The important class of spatio-temporal systems that evolve over both space and time Many case study examples from modelling space weather, through identification of a model of the visual processing system of fruit flies, to tracking causality in EEG data are all included to demonstrate how easily the methods can be applied in practice and to show the insight that the algorithms reveal even for complex systems NARMAX algorithms provide a fundamentally different approach to nonlinear system identification and signal processing for nonlinear systems. NARMAX methods provide models that are transparent, which can easily be analysed, and which can be used to solve real problems. This book is intended for graduates, postgraduates and researchers in the sciences and engineering, and also for users from other fields who have collected data and who wish to identify models to help to understand the dynamics of their systems.

Download or read book Schr dinger Equations in Nonlinear Systems written by Wu-Ming Liu and published by Springer. This book was released on 2019-03-20 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schrödinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of matter-wave solitons in the network. In the context of Bose–Einstein condensates (BECs), the book analyzes the dynamical properties of NLS equations with the external potential of different types, which govern the dynamics of modulated matter-waves in BECs with either two-body interactions or both two- and three-body interatomic interactions. It also discusses the method of investigating both the well-posedness and the ill-posedness of the boundary problem for linear and nonlinear Schrödinger equations and presents new results. Using simple examples, it then illustrates the results on the boundary problems. For both nonlinear transmission networks and Bose–Einstein condensates, the results obtained are supplemented by numerical calculations and presented as figures.